Math Envy

Twenty-three Problems in Systems Neuroscience grew out of a
symposium held in Dresden in 2000, inspired by an address given by
the great geometrist David Hilbert 100 years earlier. In his speech,
Hilbert commemorated the start of the 20th century by delivering
what is now regarded as one of the most influential mathematical
expositions ever made. He outlined 23 essential problems that not
only organized subsequent research in the field, but also clearly
reflected Hilbert's axiomatic approach to the further development of
mathematics. Anticipating his own success, he began, "Who of us
would not be glad to lift the veil behind which the future lies
hidden; to cast a glance at the next advances of our science and at
the secrets of its development during future centuries?"

I take seriously the premise represented in this new volume's title
and preface that it is intended to "serve as a source of
inspirations for future explorers of the brain." Unfortunately,
if the contributors sought to exert a "Hilbertian"
influence on the field by highlighting 23 of the most important
problems in systems neuroscience, they have, in my opinion, failed.
In failing, however, this book clearly illustrates fundamental
differences between neuroscience (and biology in general) today and
mathematics (and physics) in 1900.

Implicit in Hilbert's approach was the necessity for some type of
formal structure underlying the problems at hand, allowing other
investigators to understand their natures and then collaboratively
explore a general path to their solutions. Yet there is little
consistency in the form of the problems presented in this book.
Instead, many (perhaps most) of the chapters are organized, at best,
around vague questions such as "How does the cerebral cortex
work?" At worst, the authors simply recount what is, in effect,
a story promoting their own point of view.

The very first chapter, by Gilles Laurent, is a good example of the
latter. After starting with a well-worn plea for considering the
results of the nonmammalian, nonvisual systems he works on, Laurent
summarizes a series of experiments (many of them his own) supporting
his now-well-known position regarding the importance of synchrony in
neuronal coding. This chapter could have presented a balanced
discussion of the important questions surrounding the nature of the
neural code (as attempted in one chapter by David McAlpine and Alan
R. Palmer and in another by C. van Vreeswijk), or even referenced
and discussed some of the recently published papers questioning
Laurent's interpretations. Instead, the author chose to attempt to
convince us of his own particular solution.

I don't mean to pick on Laurent, as his chapter takes the standard
form of symposia volumes; rather, his approach illustrates the
general point that much of "systems neuroscience" (and
neuroscience in general) revolves around this kind of storytelling.
The chapter by Bruno A. Olshausen and David J. Field makes this
point explicitly, suggesting that our current "story
based" view of the function of the well-studied visual cortex
depends on (1) a biased sampling of neurons, (2) a bias in the kind
of stimuli we present and (3) a bias in the kinds of theories we
like to construct.

In fairness, several chapters do attempt to address real problems in
a concise and unbiased way. The chapter by L. F. Abbott, for
example, positing, I think correctly, that the control of the flow
of information in neural systems is a central (and unsolved)
problem, is characteristically clear, circumscribed and open-minded.
Refreshingly, Abbott's introduction states, "In the spirit of
this volume, the point of this contribution is to raise a question,
not to answer it. . . . I have my prejudices, which will become
obvious, but I do not want to rule out any of these as candidates,
nor do I want to leave the impression that the list is complete or
that the problem is in any sense solved." Given his physics
background, Abbott may actually understand enough about Hilbert's
contribution to have sought its spirit. Most chapters, however,
require considerable detective work, and probably also a
near-professional understanding of the field, to find anything
approaching Hilbert's enumeration of fundamental research problems.

In some sense I don't think the authors are completely to blame.
Although many are prominent in the field, this lack of focus on more
general and well-defined problems is, I believe, endemic in biology
as a whole. Although this may slowly be changing, the question of
how and even whether biology can move from a fundamentally
descriptive, story-based science to one from which Hilbertian-style
problems can be extracted may be the problem in systems
neuroscience. A few chapters do briefly raise this issue. For
example, in their enjoyable article on synesthesia, V. S.
Ramachandran and Edward M. Hubbard identify their approach as not
fashionable in psychology partly because of "the lingering
pernicious effect of behaviorism" and partly because
"psychologists like to ape mature quantitative
physics—even if the time isn't ripe."

Laurenz Wiskott, in his chapter on possible mechanisms for size and
shift invariance in visual (and perhaps other) cortices, raises what
may be the more fundamental question as to whether biology is even
amenable to the form of quantification and explanation that has been
so successful in physics:

Either the brain solves all invariance problems in a similar way
based on a few basic principles or it solves each invariance problem
in a specific way that is different from all others. In the former
case [asking] the more general question would be appropriate. . . .
In the latter case, that is, if all invariance problems have their
specific solution, the more general question would indeed be a set
of questions and as such not appropriate to be raised and discussed here.

He then moderates the dichotomy by stating diplomatically,
"There is, of course, a third and most likely alternative, and
that is that the truth lies somewhere between these two
extremes." Thus, Wiskott leaves unanswered the fundamental
question about the generality of brain mechanisms or computational
algorithms. As in mathematics 100 years ago, answering basic
questions in systems neuroscience is tied up in assumptions
regarding appropriate methodology. For Hilbert's colleagues, this
was obvious and constituted much of the debate following his
address; this fundamental issue, however, is only rarely discussed
in biology.

Indeed, I want to be careful not to give the impression that these
kinds of big-picture issues are given prominence in this
volume—they are not. Rather, as is typical for books generated
by these kinds of symposia, many of the chapters are simply filled
with the particular details of a particular subject, although
several authors should be commended for at least discussing their
favorite systems in several species. However, given the lack of
overall coordination, one wonders what impact this volume will have.

One way to gauge the answer is to look for evidence that the meeting
presentations influenced the other participants. As an exercise, I
summarized the major points and concerns each author raised in their
chapters and then checked that list against the assumptions and
assertions made by the other authors writing on similar subjects.
The resulting tally, I would assert, provides very little evidence
that these authors attended the same meeting—or perhaps even
that they are part of the same field!

For example, the article titled "What Is Fed Back," by
Jean Bullier, identifies, I think correctly, what will become a
major shift in thinking about how brains are organized. As Bullier
notes, there is growing evidence that the internal state of the
brain has a much more profound effect on the way the brain processes
sensory information than previously suspected. Yet this fundamental
issue is scarcely mentioned in the other chapters, quite a few of
which are firmly based on the old feed-forward
"behaviorist" model of brain function. Similarly, the
chapter by Olshausen and Field is followed immediately by a paper by
Steven W. Zucker on visual processing that depends on many of the
assumptions that Olshausen and Field call into question.

One hundred years ago, Hilbert's 23 questions organized a field. The
chapters in this book make pretty clear that we are still very far
away from having a modern-day Hilbert or even a committee of
"experts" come up with a list of 23 fundamental questions
that are accepted, or perhaps even understood, by the field of
neuroscience as a whole.